The specific non-mathematics courses that use the preparation of developmental mathematics will vary widely among colleges. For our purposes, we can group these into 3 basic categories of courses that commonly use developmental mathematics as preparation: ·Science (biology and chemistry in particular) ·Technology (biotechnology, electronics, and information technology in particular) ·Business and social science (accounting and economics in particular)
Less is known about the mathematical needs of this last category; the majority of what follows comes from the first two categories.
Basic Skills: Students need to be able to
Use estimation skills with decimals and fractions (AASMATH page 4) (with an emphasis not on a particular method of estimating i.e. frontend rounding, but more of a sense of how to make estimation work for them by modifying the procedure as needed.)
Have competence in solving linear equations (AASMATH page 5)
Have competence in solving 2 variable systems (AASMATH page 6)
Use estimation and computational skills with perimeter, area, and volume involving irregular shapes (AASMATH page 7)
Use of degree-minutes-seconds measure of angles (AASMATH page 7) - only needed for the right triangle topic it seems to me
Use of right triangle trig -- in particular, the 3 basic functions (AASMATH page 7) - I don't think this is a basic skill.
Evaluate Formulas (given all inputs, calculate the output)
Use units appropriately for measures of length, area and volume
Convert measures (linear, area, liquid, and volume) within each system (US, Metric); perform simple conversions between systems Make mental calculations with numbers such as 10%, 1/3, 1/2, 150% Use large and small numbers efficiently Create linear models from two data points, or best-fit models (with technology) from more points, and use to interpolate and predict.
Concepts: Students need to be able to
Use Geometric Models: Use geometric concepts to draw pictures of problem scenarios (AASMATH page 7)
Use Data Analysis: Use measures of central tendency, measures of variation, and mathematical models to explain and/or interpret data (AASMATH page 7)
Use Descriptive statistics, conditional probability and regression analysis (CF Biology page 2)
Use Statistical graphs & charts to identify data and interpret their meaning (“Use” means to read information from the display)
Be able to collect, organize, and display (discrete or continuous) data using a spreadsheet, and use the spreadsheet to create an appropriate chart or graph Observe and describe trends in numerical data
Use Mathematical Models: Understand variables and parameters (CF Biology page 2)
Use Graphical Representations: Use graphical representation of data in a variety of formats (histograms, scatter plots, pie charts, log-log and semi-log graphs (CF Biology page 2)
Understand concepts used with data, such as 'precision', 'significant digits', 'significance' and 'error'. (cf_biology page 2)
Use Rate of Change: use f(b)-f(a)/b-a and interpret results within the context of a scenario
Use Slope: Interpret slope in diverse settings and types of functions (AASMATH page 7) Use Counting Techniques Use Basic Rules of Probability Use Algorithms (using, not creating or programming)
Use Mathematics of finance (such as future value and monthly payment)
Functions and Modeling: Students need to be able to
Relate graphs and functions -- graphing has a very high emphasis (AASMATH page 6)
Graph (precisely with technology and to sketch without technology) all elementary functions (linear and nonlinear) (AASMATH page 6)
Apply linear, exponential and logarithmic functions given in symbolic form (CF Biology page 2)
Model data with linear, exponential and logarithmic functions and use those models to make predictions and decisions (CF Biology page 2)
Use the graphs of sine and cosine functions, and identify their periodic nature (CF Biology page 2)
Know the distinction between discrete and continuous functions, and recognize when each is appropriate
SCANS: Secretary's Commission on Achieving the Necessary Skills - (non math expectations)
Society for College Science Teachers … contact them for input? [Jack: I have tried, without any success.]
COMAP ... limited, as these materials were written to show modeling for students -- as opposed to identifying skills or modeling that are needed for a discipline or course. They have a 'developmental math' textbook (in 2 parts), and the content reinforces the items already listed above.
· Science (biology and chemistry in particular)
· Technology (biotechnology, electronics, and information technology in particular)
· Business and social science (accounting and economics in particular)
Less is known about the mathematical needs of this last category; the majority of what follows comes from the first two categories.
Basic Skills: Students need to be able to
Use estimation skills with decimals and fractions (AASMATH page 4) (with an emphasis not on a particular method of estimating i.e. frontend rounding, but more of a sense of how to make estimation work for them by modifying the procedure as needed.)
Have competence in solving linear equations (AASMATH page 5)
Have competence in solving 2 variable systems (AASMATH page 6)
Use estimation and computational skills with perimeter, area, and volume involving irregular shapes (AASMATH page 7)
Use of degree-minutes-seconds measure of angles (AASMATH page 7) - only needed for the right triangle topic it seems to me
Use of right triangle trig -- in particular, the 3 basic functions (AASMATH page 7) - I don't think this is a basic skill.
Evaluate Formulas (given all inputs, calculate the output)
Use units appropriately for measures of length, area and volume
Convert measures (linear, area, liquid, and volume) within each system (US, Metric); perform simple conversions between systems
Make mental calculations with numbers such as 10%, 1/3, 1/2, 150%
Use large and small numbers efficiently
Create linear models from two data points, or best-fit models (with technology) from more points, and use to interpolate and predict.
Concepts: Students need to be able to
Use Geometric Models: Use geometric concepts to draw pictures of problem scenarios (AASMATH page 7)
Use Data Analysis: Use measures of central tendency, measures of variation, and mathematical models to explain and/or interpret data (AASMATH page 7)
Use Descriptive statistics, conditional probability and regression analysis (CF Biology page 2)
Use Statistical graphs & charts to identify data and interpret their meaning (“Use” means to read information from the display)
Be able to collect, organize, and display (discrete or continuous) data using a spreadsheet, and use the spreadsheet to create an appropriate chart or graph
Observe and describe trends in numerical data
Use Mathematical Models: Understand variables and parameters (CF Biology page 2)
Use Graphical Representations: Use graphical representation of data in a variety of formats (histograms, scatter plots, pie charts, log-log and semi-log graphs (CF Biology page 2)
Understand concepts used with data, such as 'precision', 'significant digits', 'significance' and 'error'. (cf_biology page 2)
Use Rate of Change: use f(b)-f(a)/b-a and interpret results within the context of a scenario
Use Slope: Interpret slope in diverse settings and types of functions (AASMATH page 7)
Use Counting Techniques
Use Basic Rules of Probability
Use Algorithms (using, not creating or programming)
Use Mathematics of finance (such as future value and monthly payment)
Functions and Modeling: Students need to be able to
Relate graphs and functions -- graphing has a very high emphasis (AASMATH page 6)
Graph (precisely with technology and to sketch without technology) all elementary functions (linear and nonlinear) (AASMATH page 6)
Apply linear, exponential and logarithmic functions given in symbolic form (CF Biology page 2)
Model data with linear, exponential and logarithmic functions and use those models to make predictions and decisions (CF Biology page 2)
Use the graphs of sine and cosine functions, and identify their periodic nature (CF Biology page 2)
Know the distinction between discrete and continuous functions, and recognize when each is appropriate
REFERENCES:
"CF Biology" refers to MAA CRAFTY Biology http://www.maa.org/mtc/CF_Biology.pdf
"AASMATH" refers to "The Vision" project with MAA on voices of the partner disciplines:
http://www.aasmath.amatyc.org/webvision.pdf )
Possible additional sources:
SCANS: Secretary's Commission on Achieving the Necessary Skills - (non math expectations)
Society for College Science Teachers … contact them for input? [Jack: I have tried, without any success.]
COMAP ... limited, as these materials were written to show modeling for students -- as opposed to identifying skills or modeling that are needed for a discipline or course. They have a 'developmental math' textbook (in 2 parts), and the content reinforces the items already listed above.